3.2: Forms of a Linear Equation | Algebra 1 Honors

How it works

Slope-intercept form displays slope and vertical intercept directly. Point-slope form is useful when a point and slope are known. Standard form can reveal intercepts by setting one variable to zero. Converting between forms changes the representation, not the line.

y=mx+b,\qquad y-y_1=m(x-x_1)

Worked examples

Example 1

Write the line with slope $\displaystyle 3$ through $\displaystyle (2,1)$ .

Point-slope form gives $\displaystyle y-1=3(x-2)$ . Simplifying gives $\displaystyle y=3x-5$ .

Example 2

Find the intercepts of $\displaystyle 2x+3y=12$ .

For $\displaystyle y=0$ , $\displaystyle x=6$ . For $\displaystyle x=0$ , $\displaystyle y=4$ . The intercepts are $\displaystyle (6,0)$ and $\displaystyle (0,4)$ .

Problems

Problem 3.2.1

Write a slope-intercept equation for slope $\displaystyle -2$ and y-intercept $\displaystyle 5$ .

Show worked solution

Substitute the slope and intercept into $\displaystyle y=mx+b$ : $\displaystyle y=-2x+5$ .

Problem 3.2.2

Write an equation through $\displaystyle (1,4)$ with slope $\displaystyle 2$ .

Show worked solution

$\displaystyle y-4=2(x-1)$ , so $\displaystyle y=2x+2$ .

Problem 3.2.3

Write an equation for the graphed line using its intercepts.

A line meets the vertical axis at 3 and the horizontal axis at 3. — Use the two intercepts to describe the line.

Show worked solution

The intercepts are $\displaystyle (0,3)$ and $\displaystyle (3,0)$ . Its slope is $\displaystyle -1$ , so $\displaystyle y=-x+3$ .

A line meets the vertical axis at 3 and the horizontal axis at 3. The equation is y = −x + 3. — The equation is y = −x + 3.

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 3.2.1

Problem 3.2.2

Problem 3.2.3

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