MATH SOLVE

9 months ago

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

Accepted Solution

A:

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.Β

Standard form:

Ax + Bx = C.Β

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)

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.Β

Standard form:

Ax + Bx = C.Β

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)