QuestionFind the line equation with slope $\frac{2}{5}$ through the point $(7,-2)$ .

Studdy Solution

STEP 1

Assumptions1. The slope of the line is $\frac{}{5}$ . The line passes through the point $(7,-)$ 3. We are using the slope-intercept form of the line equation, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

We know the slope $m$ and a point $(x1, y1)$ on the line. We can use the point-slope form of the line equation to write the equation of the line. The point-slope form is $y - y1 = m(x - x1)$ .

STEP 3

Plug in the given values for the slope and the point into the point-slope form of the line equation.
$y - (-2) = \frac{2}{5}(x -7)$

STEP 4

implify the equation by removing the double negative on the left side.
$y +2 = \frac{2}{}(x -7)$

STEP 5

istribute the $\frac{2}{5}$ on the right side of the equation.
$y +2 = \frac{2}{5}x - \frac{14}{5}$

STEP 6

Subtract2 from both sides of the equation to isolate $y$ on the left side. Remember that2 is equivalent to $\frac{10}{5}$ .
$y = \frac{2}{5}x - \frac{14}{5} - \frac{10}{5}$

STEP 7

implify the right side of the equation.
$y = \frac{2}{5}x - \frac{24}{5}$ The equation of the line with a slope of $\frac{2}{5}$ that passes through the point $(7,-2)$ is $y = \frac{2}{5}x - \frac{24}{5}$ .

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