Question $3^{\text {rd }}$ point on the line: You Try 3: Given the point $(-3,-1)$ and slope $\qquad$ 5 Find a second point on the line that lies to the right of the given point.

Studdy Solution

STEP 1

1. We are given a point $(-3, -1)$ on a line.
2. The slope of the line is 5.
3. We need to find a second point on the line that lies to the right of the given point.

STEP 2

1. Understand the slope-intercept form of a line.
2. Use the slope to find the change in $y$ for a given change in $x$ .
3. Calculate the coordinates of the second point.

STEP 3

Understand the slope-intercept form of a line.
The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. However, since we are given a point and a slope, we can use the point-slope form: $y - y_1 = m(x - x_1)$ .

STEP 4

Use the slope to find the change in $y$ for a given change in $x$ .
The slope $m = 5$ tells us that for every increase of 1 in $x$ , $y$ increases by 5.

STEP 5

Calculate the coordinates of the second point.
Since we need a point to the right of $(-3, -1)$ , we can increase $x$ by 1.
New $x$ -coordinate: $-3 + 1 = -2$ .
Using the slope, calculate the new $y$ -coordinate:
Change in $y$ = slope $\times$ change in $x = 5 \times 1 = 5$ .
New $y$ -coordinate: $-1 + 5 = 4$ .
Thus, the second point on the line is $(-2, 4)$ .

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