Consider the given equation of a line.
2x+3y=9
When lines are parallel, they have the same slope. Because of this, we know that all lines that are parallel to the line whose equation is given will have the same slope. To help us identify the slope of this line, let's first convert it into slope-intercept form, y=mx+ b, where m is the slope and (0, b) is the y-intercept.
With this, we can more easily identify the slope m and y-intercept b.
y=-2/3x+ 3
We can write a general equation in slope-intercept form for these lines.
y=-2/3x+ b
We are asked to write the equation of a line parallel to the one with given equation that passes through the point ( - 1, 4). By substituting this point into the above equation for x and y, we will be able to solve for the y-intercept b of the parallel line.
