Solving Systems By Graphing SlopeIntercept Form y mx

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: 1 st: graph the y-intercept (the b) y=½x+3 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 • Standard form for the equation of a line Ax = C • Finds the x-intercept +By = C • 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: 3 x – 4 y = 24 3 x – 4(0) = 24 3 x = 24 3 3 x=8 • 1 st find the x-int • Set y = 0 • Solve for x

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

Graph: 1 st: graph the x-intercept: 8 3 x – 4 y = 24 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: 1 st: graph the 1 st equation y=½x+3 2 nd: graph the 2 nd equation y = 4 x - 4 3 rd: the solution is the point of intersection Our Solution is (2, 4)