Answer
$a. \space y = -\frac{3}{2}x + 9;\quad \text{slope:} -\frac{3}{2}; \quad \text{y-intercept: }9$
$b. \space -5y = 7x + 35; \quad \text{slope: } -\frac{7}{5}; \quad \text{y-intercept: } -7$
Work Step by Step
a. This equation of a line is written in standard form. We are asked to rewrite this line in slope-intercept form, which is given by the following formula:
$y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.
Rewrite the equation by isolating the $y$ term. First, subtract $3x$ from each side of the equation:
$$2y = -3x + 18$$
Divide both sides of the equation by $2$ to isolate $y$:
$$y = -\frac{3}{2}x + 9$$
So the slope of this line is the coefficient of $x$; in this case, the slope of this line is $-\frac{3}{2}$.
The $y$-intercept is the value of the constant. In this case, the $y$-intercept is $9$.
b. This equation of a line is written in standard form. We are asked to rewrite this line in slope-intercept form, which is given by the following formula:
$y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.
Rewrite the equation by isolating the $y$ term. First, add $7x$ to each side of the equation:
$$-5y = 7x + 35$$
Divide both sides of the equation by $-5$ to isolate $y$:
$$y = -\frac{7}{5}x - 7$$
So the slope of this line is the coefficient of $x$; in this case, the slope of this line is $-\frac{7}{5}$.
The $y$-intercept is the value of the constant. In this case, the $y$-intercept is $-7$.
