Question3) What is the linear equation of a line with slope $\frac{2}{3}$ and passes through the point $(-6,5)$ ?

Studdy Solution

STEP 1

1. We are given the slope of the line, $m = \frac{2}{3}$ .
2. The line passes through the point $(-6, 5)$ .
3. We need to find the linear equation of the line in slope-intercept form $y = mx + b$ .

STEP 2

1. Use the point-slope form of a linear equation.
2. Substitute the given slope and point into the point-slope form.
3. Simplify to convert the equation into slope-intercept form.

STEP 3

Use the point-slope form of a linear equation, which is:
$y - y_1 = m(x - x_1)$
where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

STEP 4

Substitute the given slope $m = \frac{2}{3}$ and the point $(-6, 5)$ into the point-slope form:
$y - 5 = \frac{2}{3}(x + 6)$

STEP 5

Simplify the equation to convert it into slope-intercept form $y = mx + b$ .
Distribute the slope on the right side:
$y - 5 = \frac{2}{3}x + \frac{2}{3} \times 6$
$y - 5 = \frac{2}{3}x + 4$
Add 5 to both sides to solve for $y$ :
$y = \frac{2}{3}x + 4 + 5$
$y = \frac{2}{3}x + 9$
The linear equation of the line is:
$y = \frac{2}{3}x + 9$

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