Solving Systems By Graphing. Slope-Intercept Form y = mx + b m = slope b = y-intercept Slope-Intercept form for the equation of a line Slope = rise run.

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Solving Systems By Graphing

Slope-Intercept Form y = mx + b m = slope b = y-intercept Slope-Intercept form for the equation of a line Slope = rise run y-intercept is the point where the line crosses the y-axis

Graph: y = ½ x st : graph the y-intercept (the b) 2 nd : follow the slope (rise over run) 3 rd : connect the dots We’re graphing lines, so don’t forget to draw a line!

Standard Form Ax + By = C Ax = C +By = C Standard form for the equation of a line Finds the x-intercept Finds the y-intercept

Definition of an Intercept An intercept is the point where a line crosses either of the axes. When the line crosses the y-axis, it is called the y-intercept When the line crosses the x-axis, it is called the x-intercept The coordinates for a y-intercept comes in the form (0,y) The coordinates for an x-intercept comes in the form (x, 0)

Graphing Standard Form Graph: 3x – 4y = 24 3x – 4(0) = 24 3x = x = 8 1 st find the x-int Set y = 0 Solve for x

Graphing Standard Form 3(0) – 4y = 24 -4y = y = -6 Now solve for y Set x = 0 Now graph the intercepts with those values that we found

Graph: 3x – 4y = 24 1 st : graph the x-intercept: 8 2 nd : graph the y-intercept: -6 3 rd : connect the dots We’re graphing lines, so don’t forget to draw a line!

Solving Systems of Equations A system of equations is 2 or more equations using the same 2 or more variables Can be solved 3 ways –By graphing –By substitution –By elimination We will focus on the graphing part now The solution to a system is the set of all points both lines have in common

Solving Systems of Equations There are 3 possibilities when solving a system of equations. –There can be 1 solution (intersecting lines) –There can be no solution (parallel lines) –There can be infinitely many solutions (same line) Let’s see an example of each

Solve: y = ½ x + 3 y = 4x st : graph the 1 st equation 2 nd : graph the 2 nd equation 3 rd : the solution is the point of intersection Our Solution is (2,4)

Solve: y = 2x + 3 y = 2x – 1 1 st : graph the 1 st equation 2 nd : graph the 2 nd equation 3 rd : These are parallel lines There is no solution

Solve: y = ¾ x – 2 1 st : graph the 1 st equation 2 nd : graph the 2 nd equation 3 rd : These are the same line There are infinitely many solutions