QuestionFind the $y$ -intercept $r$ of the line through points $(-3, \frac{5}{2})$ and $(4, -1)$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the points $\left(-3 ; \frac{5}{}\right)$ and $(4 ;-1)$ . . The line intercepts the y-axis at $(0 ; r)$ .
3. We need to find the value of $r$ .

STEP 2

The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ can be calculated using the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Substitute the given points into the slope formula $m = \frac{-1 - \frac{5}{2}}{ - (-3)}$

STEP 4

implify the numerator and denominator separately $m = \frac{-\frac{7}{2}}{7}$

STEP 5

implify the fraction to find the slope $m = -\frac{1}{2}$

STEP 6

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

STEP 7

Substitute the slope and one of the points into the equation of the line. We'll use the point $(4, -1)$ $-1 = -\frac{1}{2} \cdot4 + b$

STEP 8

olve for $b$ $b = -1 +2 =1$

STEP 9

The y-intercept of the line is $(, b)$ , so $r = b$ .

STEP 10

Substitute $b$ into $r$ $r =$ So, the correct answer is c..

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