Question

Which equation is the equation of the line, in point-slope form, that has a slope of 1.9 and passes through the point begin (4.5, -1.4)?

Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (-8,1)?

Answer 1

In point-slope form, the equation for a line with a slope of 1.9 through (4.5, -1.4) is y + 1.4 = 1.9(x - 4.5), and for a slope of 2 through (-8,1), it is y - 1 = 2(x + 8). The slope between (1, 0.1) and (7, 26.8) is approximately 4.5.

Step-by-step explanation:

The equation of the line in point-slope form that has a slope of 1.9 and passes through the point (4.5, -1.4) can be written as y - (-1.4) = 1.9(x - 4.5), which simplifies to y + 1.4 = 1.9(x - 4.5). For the line with a slope of 2 that passes through the point (-8,1), the equation is y - 1 = 2(x + 8), which simplifies to y - 1 = 2x + 16.

The slope, denoted as m, of a line passing through two points can be found using the formula m = (y2 - y1) / (x2 - x1). For points (1, 0.1) and (7, 26.8), the slope calculation would be m = (26.8 - 0.1) / (7 - 1), which equals 4.45 when rounded to two decimal places, so the correct answer is b. 4.5.

Answer 2

(a)
`y+1.4=1.9(x-4.5)`

(b)
`y-1=2(x+8)`

Step-by-step explanation:

If a line passes through a points
`(x_1,y_1)` with slope m, then the point slope form of the line is

`y-y_1=m(x-x_1)`

It is given that the slope of the line is 1.9 and it passes through the point (4.5, -1.4). So, the equation of line in point-slope form is

`y-(-1.4)=1.9(x-4.5)`

`y+1.4=1.9(x-4.5)`

It is given that the slope of the line is 2 and it passes through the point (-8,1). So, the equation of line in point-slope form is

`y-1=2(x-(-8))`

`y-1=2(x+8)`