QuestionFind the $x$ intercept $r$ of the line through points $(2, -3)$ and $(4, 4)$ . What is $r$ ?

Studdy Solution

STEP 1

Assumptions1. The line passes through the points $( ;-3)$ and $(4 ;4)$ . . The $x$ intercept of this line has coordinates $(r ;0)$ .

STEP 2

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Substitute the given points into the formula to find the slope.
$m = \frac{ - (-3)}{ -2}$

STEP 4

Calculate the slope of the line.
$m = \frac{7}{2}$

STEP 5

The equation of a line in slope-intercept form is given by $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept.

STEP 6

Substitute the slope and one of the points into the equation to find the y-intercept.
$-3 = \frac{}{2} \cdot2 + c$

STEP 7

olve the equation for $c$ to find the y-intercept.
$c = -3 - \frac{7}{2} \cdot2 = -7$

STEP 8

The equation of the line is then $y = \frac{7}{2}x -7$

STEP 9

The x-intercept of a line is the x-coordinate where the line crosses the x-axis (where $y =$ ). So, set $y =$ in the equation of the line and solve for $x$ .
$= \frac{7}{2}x -7$

STEP 10

olve the equation for $x$ to find the x-intercept.
$x = \frac{7}{2}$ So, $r = \frac{7}{2}$ .
The correct answer is (a) $\frac{7}{2}$ .

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QuestionFind the $x$ intercept $r$ of the line through points $(2, -3)$ and $(4, 4)$ . What is $r$ ?

Studdy Solution

STEP 1

Assumptions1. The line passes through the points $( ;-3)$ and $(4 ;4)$ . . The $x$ intercept of this line has coordinates $(r ;0)$ .

STEP 2

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Substitute the given points into the formula to find the slope.
$m = \frac{ - (-3)}{ -2}$

STEP 4

Calculate the slope of the line.
$m = \frac{7}{2}$

STEP 5

The equation of a line in slope-intercept form is given by $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept.

STEP 6

Substitute the slope and one of the points into the equation to find the y-intercept.
$-3 = \frac{}{2} \cdot2 + c$

STEP 7

olve the equation for $c$ to find the y-intercept.
$c = -3 - \frac{7}{2} \cdot2 = -7$

STEP 8

The equation of the line is then $y = \frac{7}{2}x -7$

STEP 9

The x-intercept of a line is the x-coordinate where the line crosses the x-axis (where $y =$ ). So, set $y =$ in the equation of the line and solve for $x$ .
$= \frac{7}{2}x -7$

STEP 10

olve the equation for $x$ to find the x-intercept.
$x = \frac{7}{2}$ So, $r = \frac{7}{2}$ .
The correct answer is (a) $\frac{7}{2}$ .

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QuestionFind the xxx intercept rrr of the line through points (2,−3)(2, -3)(2,−3) and (4,4)(4, 4)(4,4). What is rrr?

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (;−3)( ;-3)(;−3) and (4;4)(4 ;4)(4;4). . The xxx intercept of this line has coordinates (r;0)(r ;0)(r;0).

STEP 2

The slope of a line passing through two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Substitute the given points into the formula to find the slope.m=−(−3)−2m = \frac{ - (-3)}{ -2}m=−2−(−3)​

STEP 4

Calculate the slope of the line.m=72m = \frac{7}{2}m=27​

STEP 5

The equation of a line in slope-intercept form is given byy=mx+cy = mx + cy=mx+cwhere mmm is the slope and ccc is the y-intercept.

STEP 6

Substitute the slope and one of the points into the equation to find the y-intercept.−3=2⋅2+c-3 = \frac{}{2} \cdot2 + c−3=2​⋅2+c

STEP 7

olve the equation for ccc to find the y-intercept.c=−3−72⋅2=−7c = -3 - \frac{7}{2} \cdot2 = -7c=−3−27​⋅2=−7

STEP 8

The equation of the line is theny=72x−7y = \frac{7}{2}x -7y=27​x−7

STEP 9

The x-intercept of a line is the x-coordinate where the line crosses the x-axis (where y=y =y=). So, set y=y =y= in the equation of the line and solve for xxx.=72x−7 = \frac{7}{2}x -7=27​x−7

STEP 10

olve the equation for xxx to find the x-intercept.x=72x = \frac{7}{2}x=27​So, r=72r = \frac{7}{2}r=27​.The correct answer is (a) 72\frac{7}{2}27​.

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QuestionFind the $x$ intercept $r$ of the line through points $(2, -3)$ and $(4, 4)$ . What is $r$ ?

Assumptions1. The line passes through the points $( ;-3)$ and $(4 ;4)$ . . The $x$ intercept of this line has coordinates $(r ;0)$ .

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

Substitute the given points into the formula to find the slope.
$m = \frac{ - (-3)}{ -2}$

Calculate the slope of the line.
$m = \frac{7}{2}$

The equation of a line in slope-intercept form is given by $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept.

Substitute the slope and one of the points into the equation to find the y-intercept.
$-3 = \frac{}{2} \cdot2 + c$

olve the equation for $c$ to find the y-intercept.
$c = -3 - \frac{7}{2} \cdot2 = -7$

The equation of the line is then $y = \frac{7}{2}x -7$

The x-intercept of a line is the x-coordinate where the line crosses the x-axis (where $y =$ ). So, set $y =$ in the equation of the line and solve for $x$ .
$= \frac{7}{2}x -7$

olve the equation for $x$ to find the x-intercept.
$x = \frac{7}{2}$ So, $r = \frac{7}{2}$ .
The correct answer is (a) $\frac{7}{2}$ .