Math

QuestionFind the intercepts of the line given by y3=5(x2)y-3=5(x-2). yy-intercept: (,)(\quad, \quad), xx-intercept: (,)(, \quad).

Studdy Solution

STEP 1

Assumptions1. We are given a linear equation in the form of yy1=m(xx1)y - y1 = m(x - x1), where mm is the slope of the line and (x1,y1)(x1, y1) is a point on the line. . We need to find the yy-intercept and the xx-intercept of the line.
3. The yy-intercept is the point where the line crosses the yy-axis. At this point, x=0x =0.
4. The xx-intercept is the point where the line crosses the xx-axis. At this point, y=0y =0.

STEP 2

First, let's find the yy-intercept. We can do this by setting x=0x =0 in the given equation and solving for yy.
y=5(02)y - =5(0 -2)

STEP 3

implify the equation to find the yy-intercept.
y3=5times2y -3 =5 \\times -2

STEP 4

Calculate the right side of the equation.
y3=10y -3 = -10

STEP 5

Add3 to both sides of the equation to solve for yy.
y=10+3y = -10 +3

STEP 6

Calculate the yy-intercept.
y=y = -So, the yy-intercept is ()(-).

STEP 7

Next, let's find the xx-intercept. We can do this by setting y=0y =0 in the given equation and solving for xx.
03=5(x2)0 -3 =5(x -2)

STEP 8

implify the equation to find the xx-intercept.
3=5(x2)-3 =5(x -2)

STEP 9

Divide both sides of the equation by5 to isolate xx.
x2=3/5x -2 = -3/5

STEP 10

Add2 to both sides of the equation to solve for xx.
x=3/5+2x = -3/5 +2

STEP 11

Calculate the xx-intercept.
x=7/5x =7/5So, the xx-intercept is (7/5)(7/5).
The intercepts of the line areyy-intercept (0,7)(0, -7)xx-intercept (7/5,0)(7/5,0)

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