Question

What is an equation of the line that is parallel to y = 5x - 7 and passes through (1, 11)

Answer 1

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

y = 5x - 7     The slope is 5, so the parallel line's slope is also 5.

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

y = 5x + b   To find b, plug in the point (1, 11) into the equation, the isolate/get the variable "b" by itself in the equation

11 = 5(1) + b    Subtract 5 on both sides to get "b" by itself

11 - 5 = 5 - 5 + b

6 = b

y = 5x + 6