2.5.1 – Writing Equations of Lines

Given certain information, we must now be able to write our own equations of graphs Still try and use the forms of linear equations we have covered so far; slope intercept and a variation of standard form

Slope-Intercept To write an equation in the form y = mx + b, all we need is a known slope (or two points to find the slope) and the y-intercept Remember, slope formula = m =

Example. Write the slope-intercept form given m = -3 and b = 4. Example. Write the slope intercept form given m = 1/3 and b = -3.

Example. Write the slope-intercept form for the equation of the line shown. Can you find a y-int? Slope?

Example. Write the slope-intercept form for the equation of the line shown. Can you find a y-int? Slope?

Point-Slope Form What is the draw back to the form y = mx + b? Can you easily use it just for any point? To help around it’s short comings, we can use what is known as point-slope form Given a point, and a slope OR two points on the line, we can determine an equation

Given the slope m and the point (x 1, y 1 ), the point slope form of an equation is: y - y 1 = m(x - x 1 ) May also do the same given two points (x 1, y 1 ) and (x 2, y 2 )

Example. Write the equation of the line that passes through the point (4, 2) and has a slope of m = -1/4 in point-slope form.

Example. Write the equation of the line that passes through the point (-3, -3) with a slope m = 2/3 in point-slope form.

Example. Write the equation of the line that passes through the point (-3, -5) and slope m = -5 in slope-intercept form – How do you get to slope-intercept form?

Example. Write an equation of the line shown in the following graph.

Assignment Pg. 97 1, 2, 13 – 23 odd, odd, 57, 58