Question

Vocabulary tell whether each linear equation is in slope-intercept form, point-slope form, or standard form.

a.y 5= -(x- 2)
b. y = -2x 5
c. y - 10 = -2(x - 1)
d.2x 4y=:12

Answer 1

Linear equations can be in slope-intercept form, point-slope form, or standard form. Equations a and c are in point-slope form, equation b is in slope-intercept form, and equation d is in standard form.

Step-by-step explanation:

When categorizing linear equations, we specifically look at their structure to determine if they are in slope-intercept form, point-slope form, or standard form.

• The slope-intercept form is written as y = a + bx, where b represents the slope and a represents the y-intercept.
• Point-slope form is written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is a specific point on the line.
• Standard form is usually written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Based on this, we can categorize each equation:

1. y = -5(x - 2) is in point-slope form since it shows a specific point (2, -5) and the slope (-5).
2. y = -2x + 5 is in slope-intercept form with a slope of -2 and a y-intercept of 5.
3. y - 10 = -2(x - 1) is also in point-slope form, showing the point (1, 10) and the slope (-2).
4. 2x + 4y = 12 is in standard form, as it is arranged with x and y on one side and the constant on the other.