Hi there!
Given an equation in point-slope form, explain how to determine the coordinates of its y-intercept.
- The y-intercept of a line occurs when x=0.
- Replace x with 0 in the equation and solve for y to find the y-intercept.
Given an equation or graph of a line, describe how to write an equation of a parallel line that goes through a given point.
- Determine the slope of the line. In slope-intercept form [tex]y=mx+b[/tex], the slope would be [tex]m[/tex], and in point-slope form [tex]y-y_1=m(x-x_1)[/tex], the slope would be [tex]m[/tex] as well. Given a graph, it would be necessary to solve for the slope. Find two points and plug them into the equation [tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}}[/tex] as [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] to solve for the slope.
- Parallel lines always have the same slope. Now that we've just solved for the slope, plug it into [tex]y=mx+b[/tex].
- Now, all that's left to solve in the equation is [tex]b[/tex]. Plug the given point into [tex]y=mx+b[/tex] along with the slope and solve for [tex]b[/tex].
- Plug both the slope and y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation.
Given an equation or graph of a line, describe how to write an equation of a perpendicular line that goes through a given point.
- Determine the slope of the line.
- Perpendicular lines always have slopes that are negative reciprocals. To determine the slope of a perpendicular line, take the slope from step 1 and find its negative reciprocal. For example, the negative reciprocal of 2 is -1/2. Plug this slope into [tex]y=mx+b[/tex].
- Now, all that's left to solve in the equation is [tex]b[/tex]. Plug the given point into [tex]y=mx+b[/tex] along with the slope and solve for [tex]b[/tex].
- Plug both the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation.
I hope this helps!
