Math / Geometry

Question16. Give the slope, $y$ -intercept and equation of the line between the two points. Put n/a if necessary. $\begin{array}{r} (0,5) \text { and }(-3,5) \\ m=\$ \end{array}$ $\qquad$ $b=$ $\qquad$ equation: $\qquad$

Studdy Solution

STEP 1

1. We are given two points: $(0, 5)$ and $(-3, 5)$ .
2. The slope $m$ , $y$ -intercept $b$ , and equation of the line are to be determined.

STEP 2

1. Determine the slope of the line.
2. Determine the $y$ -intercept.
3. Write the equation of the line.

STEP 3

Determine the slope of the line using the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(0, 5)$ and $(-3, 5)$ :
$m = \frac{5 - 5}{-3 - 0} = \frac{0}{-3} = 0$

STEP 4

Determine the $y$ -intercept. Since one of the points is $(0, 5)$ , the $y$ -intercept $b$ is:
$b = 5$

STEP 5

Write the equation of the line using the slope-intercept form $y = mx + b$ :
Since $m = 0$ and $b = 5$ , the equation is:
$y = 0 \cdot x + 5$ $y = 5$
The slope is $m = 0$ , the $y$ -intercept is $b = 5$ , and the equation of the line is:
$\boxed{y = 5}$

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