Answer
$y = -0.4x + 8.8$
Work Step by Step
The equation of the line given is in standard form, which is given by the formula $Ax + By = C$, where $A$, $B$, and $C$ are real numbers.
We will need to rewrite this equation in slope-intercept form to find its slope. The slope-intercept form is given by the formula $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Let's rewrite the equation given so that $y$ is isolated on the left side of the equation.
Subtract $2x$ from both sides of the equation:
$5y = -2x + 11$
Divide both sides of the equation by $5$ to isolate $y$:
$y = -\frac{2}{5}x + \frac{11}{5}$
Therefore, the slope of the given equation is $-\frac{2}{5}$. This is also the slope of the equation we are trying to find.
Let's plug in the slope and the point given into the point-slope form of the equation, which is given by the formula:
$y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.
Let's plug in the points into the formula:
$y - 10 = -\frac{2}{5}(x - (-3))$
Simplify:
$y - 10 = -\frac{2}{5}(x + 3)$
We are asked to write the equation in slope-intercept form, which is given by the following formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Use the distributive property:
$y - 10 = -\frac{2}{5}x - \frac{6}{5}$
Let's rewrite the equation using decimals instead of fractions:
$y - 10 = -0.4x - 1.2$
Isolate $y$ by adding $10$ to both sides of the equation:
$y = -0.4x + 8.8$
