Question

Choose the correct equation in point slope form for the line through the given points or through the given point with the given slope

Answer 1

To write an equation in point-slope form for a line, you can calculate the slope using two known points or use a given point and slope. The equation is y - Y1 = m(x - X1). Using the slope of 3 and y-intercept of 9 from Figure A1, the point-slope form equation is y - 9 = 3x.

Step-by-step explanation:

The subject of the question is Mathematics, specifically focused on the algebra of straight lines and how to write equations representing them. To choose the correct equation in point-slope form for a line, one must know either two points on the line or one point and the slope. If two points on the line are known, labeled as (X1, Y1) and (X2, Y2), the slope m can be calculated using the formula m = (Y2 - Y1) / (X2 - X1). Once the slope m is known, and one point, say (X1, Y1), the point-slope form equation can be written as y - Y1 = m(x - X1).

Using the information provided in Figure A1, the slope of the line is given as 3, and the y-intercept is 9. Therefore, the equation of the line in slope-intercept form is y = 3x + 9. From this, we can derive the point-slope form of the equation using any point on the line.

To illustrate with an example, let us use the y-intercept as our known point: (0, 9). Thus, applying the point-slope form would give us the equation y - 9 = 3(x - 0), which simplifies to y - 9 = 3x.

Answer 2

`y-3=-1(x+2)`

Step-by-step explanation:

The point-slope form of the equation of a line is generally given as;

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

where m = the slope of the line

y1 = y-coordinate of the one point

x1 = x-coordinate of the one point

Given the slope of the line as m = -1 and the point (-2, 3) where x1 = -2 and y1 = 3, let's go ahead and substitute these given values into the point-slope formula to obtain the required equation as seen below;

`\begin{gathered} y-3=-1\lbrack x-(-2)\rbrack \\ y-3=-1(x+2) \end{gathered}`