Question

How do you graph a linear function in slope-intercept, point-slope, and standard form?

Answer 1

To graph a linear function in slope-intercept, point-slope, and standard form, determine the slope and y-intercept, plot the y-intercept, find additional points using the slope, and connect the points with a line.

Step-by-step explanation:

To graph a linear function in slope-intercept form, start by identifying the slope and y-intercept from the equation. The slope, represented by 'm', determines the steepness of the line, while the y-intercept, represented by 'b', gives the point where the line crosses the y-axis. Plot the y-intercept on the graph and then use the slope to find additional points. Connect the points with a straight line.

In point-slope form, start with a point on the line and the slope. Use the slope to find another point, and then connect the two points with a straight line.

In standard form, rearrange the equation to isolate 'y'. Plot two points using the x and y intercepts, and draw a line through those points.

Answer 2

Slope-intercept:
Find the slope (change in y / change in x) of the equation, and the y intercept (the point where the line crosses the x axis).
y = mx + b, where m is the slope and b is the y-intercept.

To graph, draw a line through (0,b) with slope m.

Point-slope form:
(y-b) = m(x-a), where m is the slope and (a,b) is a point the line passes through.

Find the slope, and then pick any point that lies on the line and substitute into (a,b).
To graph, start at the point (a,b), and draw a line through that point with slope m.

Standard form:
Ax + Bx = C.
Example: 2x + 3y = 24
Notice that this form does not clearly include any points, the slope, or the intercepts. So how can we easily graph it?
To graph a line written in standard form, you can simply draw a line between the y-intercept and the x-intercept.
To find the y-intercept using our example.
2x + 3y = 24
y intercept is where x=0
0 + 3y = 24
y = 8 when x=0, y-intercept = (0,8)
X-intercept, sae process but plugging in zero for y:
2x + 0 = 24
x = 12
To graph, simply draw a line that goes through (0,8) and (0,12)