Final answer:
The student's question deals with converting linear equations between point-slope and slope-intercept forms. In point-slope form, the general equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In slope-intercept form, the general equation is y = mx + b, where m is the slope and b is the y-intercept.
Step-by-step explanation:
The student's question involves various forms of linear equations and how to convert between them. This is a key concept in high school algebra.
Point Slope Form :
For any linear equation, the point-slope form is y - y1 = m(x - x1), where (x1, y1) is any point on the line and m is the slope of the line.
- a) The equation y - 3 = 2(x + 1) is already in point-slope form with the point being (-1, 3) and the slope 2.
- c) We can convert 2y - 5 = 4(x - 2) by first isolating y to get y = 2(x - 2) + 5/2. Dividing each term by 2, we have y - 5/2 = 2(x - 2), which puts it in point-slope form with the point being (2, 5/2).
- d) The equation y + 2 = -3(x - 1) is already in point-slope form with the point (1, -2) and slope -3.
Slope Intercept Form :
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept of the line.
- b) The equation y = 3x - 4 is already in slope-intercept form with a slope 3 and y-intercept -4.