Question

Solve the system of equations y=-2x+5 and y=x-1 by graphing.

Look at the first equation: y=-2x+5.
What is he slope ?____
What is the Y-intercept?_____
Look at the second equation y=x-1.

what is the slope?
What is the y-intercept?

Answer 1

To solve by graphing, you must sketch both lines. For y=-2x+5, the gradient will be -2 and the y-intercept will be 5. For y=x-1 the gradient is 1 and the y-intercept is -1. To find the solution, you just look at the point where the lines intersect (cross). The x coordinate of this should be 2. You can then put this value of x=2 into this equation y=-2(2) + 5 = -4+5=1 to get 1, or this equation: y=2-1 = 1. Notice that the x coordinate x=2 produces the value of y=1 using either of the two equations you started with. This is a good indicator you are right when it comes to linear equations of this form. This is because if two straight lines intersect (cross), they will intersect in one place only.

Answer 2

perfect. One quick question. What would the y-intercept be for the firstt equation ?

Answer 3

the y-intercept for y=-2x+5 is +5 on the y-axis.

Consider the general equation for a line: y=mx +c where m and c are numbers, m is the gradient and c is the y-intercept. If there is a '+' in front of the c then obviously the y-intercept lies on the positive y-axis, if there is a '-' in front of the c then the y-intercept lies on the negative part of the y-axis.

The number m is a little more complicated. m is the gradient and is given by m=change in y/change in x or simply m = distance up/distance along. If m = -2 then the distance up is -2 and the distance along is 1. Alternatively you could have distance up is 2 and distance along is -1, either point of view is equivalent.