Question

What is an equation of the line that passes through the point (5, 4) and is parallel to

Answer 1

Answer & Step-by-step explanation:

When two lines are parallel, their slopes are the same. To find the slope of the given equation, convert to slope-intercept form:

$y=mx+b$

• m is the slope
• b is the y-intercept, which is the value of y when the value of x is zero
• x and y are the corresponding coordinate points (x,y)

$6x-5y=15$

Solve for y. Subtract 6x from both sides:

$6x-6x-5y=15-6x\\\\-5y=-6x+15$

Divide both sides by -5:

$\frac{-5y}{-5} =\frac{-6x}{-5} +\frac{15}{-5} \\\\y=\frac{6}{5}x-3$

The slope is $\frac{6}{5}$.

Now you need to make an equation in point-slope form:

$y-y_{1}=m(x-x_{1})$

• m is the slope
• $x_{1}$ and $y_{1}$ are the coordinate points

Insert known values:

$y-4=\frac{6}{5}(x-5)$

You can use this equation, or you can convert to slope-intercept form by solving for y:

Use the distributive property:

$y-4=\frac{6}{5} x-6$

Add 4 to both sides:

$y-4+4=\frac{6}{5}x-6+4\\\\ y=\frac{6}{5}x-2$

:Done