Question

3.Write the equation in slope-intercept form for the line that passes through the given pointand is parallel to the given equation.5x + 2y = 10 and passes through (-6, 7)

Answer 1

Slope Intercept Form:

$y=mx+b$

Where

m is slope

b is y-intercept (y-axis cutting point)

Now,

We know parallel lines have equal slope.

Let's work with the line equation given to find its slope:

$\begin{gathered} 5x+2y=10 \\ 2y=-5x+10 \\ y=-\frac{5}{2}x+5 \end{gathered}$

Slope is -5/2. This will be same for our line.

So, we can write:

$y=-\frac{5}{2}x+b$

To find b, we put (-6,7) into x and y respectively and find b:

$\begin{gathered} y=-\frac{5}{2}x+b \\ 7=-\frac{5}{2}(-6)+b \\ 7=15+b \\ b=7-15 \\ b=-8 \end{gathered}$

So, final equation:

$y=-\frac{5}{2}x-8$