Algebra II Practice Questions

Question

Write an equation in slope-intercept form for the line that passes through (-3,5) and is parallel to y=-6x+1

Answer 1

A slope intercept form line equation is

y = mx + b where m is the slope

y = - 6x + 1

means that the slope of the first line is - 6

A second line is parallel to the first line. Parallel means both lines have the same slope which is - 6

A line equation that pass (-3,5) and with slope - 6

y = mx + b put x and y the numbers from the coordinate (-3,5) to find b

5 = - 6 * (-3) + b

5 = 18 + b

b = 5-18

= - 13

So the line equation that is parallel to the first line and pass (-3,5) is

y = - 6x - 13

I do have other way to find a line equation directly by this formula;

y - y1 = m (x - x1)

where x1 and y1 is the coordinate of the point that the line pass.

y - 5 = - 6 * (x - (-3))

y - 5 = - 6 * (x +3)

y - 5 = - 6x - 18 eliminate 5 from the left hand side

y = - 6x - 18 +5

y = - 6x - 13

Answer 2

Condition for parallel lines is 2 lines having the same slope: -6

So general equation in slope-intercept form for that line will be

y = -6x + b

where b is not yet found y-intercept

To find it out, "plugin" the given point into this equation. The point (-3,5) is on the line, so it should statisfy

5 = -6 (-3) + b

From this equation b = -13

So the complete equation for the line will be

y = -6 x - 13