Question

Match each linear equation with the correct description.

a) y - 7 = 2/3(x + 15) - Point-slope form
b) 6x – 3y = -51 - Standard form
c) x - 7 = 2/3(y + 15) - Slope-intercept form
d) -2/3 + y = 17 - None of the above"

Answer 1

After analyzing the given equations, it is clear that option a) is Point-slope form, option b) is Standard form, but option c) does not represent the Slope-intercept form as presented and requires rearranging, and option d) is None of the above.

Step-by-step explanation:

The student's question involves matching each linear equation to its correct description. Let's go through the options given:

• Point-slope form of a linear equation typically looks like y - y1 = m(x - x1), where m is the slope and (x1, y1) is a specific point on the line.
• Standard form is typically Ax + By = C, where A, B, and C are integers, and A should be non-negative.
• Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Based on the descriptions above, we can match the equations as follows:

1. a) y - 7 = 2/3(x + 15) - Point-slope form
2. b) 6x – 3y = -51 - Standard form
3. c) The given equation does not represent Slope-intercept form as it is incorrectly formatted; it should be rearranged to fit y = mx + b.
4. d) -2/3 + y = 17 - This is not a standard, point-slope, or slope-intercept form, hence the answer is None of the above.