You can put this solution on YOUR website! Using the slope-intercept form for a linear equation, you begin with:
.
y = mx + b
.
in which m is the slope and b is the value of y at the point where the graph intercepts
the y-axis.
.
You are told that the line graph has a slope of 3. Substitute this for m and the slope-intercept
equation becomes:
.
y = 3x + b
.
Next you are told that the point (2, -3) is on the graph. Therefore, when x = 2 and y = -3
the equation is satisfied. So you can substitute these values and solve for b. Let x = 2
and y = -3 and you get:
.
-3 = 3(2) + b
.
Multiply out the right side to get:
.
-3 = 6 + b
.
get rid of the +6 on the right side by subtracting 6 from both sides to reduce the equation to:
.
- 9 = b
.
Return to the slope-intercept form and recognize that m = 3 and b = -9 and you have the
equation:
.
y = 3x - 9
.
This is the answer. You can also use the equation:
.
.
in which and are from the given point on the equation. Substituting
2 for and -3 for and 3 for m results in the equation becoming:
.
.
which simplifies to:
.
.
Subtracting 3 from both sides to get rid of the 3 on the left side further reduces the
equation to:
.
.
which is the same answer that we got previously.
.
Hope these two ways of solving this problem are of use to you in understanding the problem
and how to get the answer.
.
(