Question

A straight line joins the points (-1, -4) and (3, 8)

i) Find the midpoint of this line
ii) Find the equation of this line. Give your answer in the form y=mx+c

Answer 1

The midpoint of the line segment joining points (-1, -4) and (3, 8) is (1, 2). The equation of the line in the form y = mx + c is y = 3x - 1, where 3 is the slope and -1 is the y-intercept.

Step-by-step explanation:

Finding the Midpoint of a Line Segment

To find the midpoint of the line segment joining the points (-1, -4) and (3, 8), we use the midpoint formula, which is the average of the x-coordinates and the y-coordinates of the two points. The formula is given by:

M = ((x1 + x2)/2, (y1 + y2)/2).

Plugging in the coordinates:

M = ((-1 + 3)/2, (-4 + 8)/2) = (2/2, 4/2) = (1, 2).

Therefore, the midpoint of the line is (1, 2).

Finding the Equation of a Line

To find the equation of a line in the form y = mx + c, we first calculate the slope (m) by taking the difference in y-coordinates divided by the difference in x-coordinates:

m = (y2 - y1) / (x2 - x1).

For our points (-1, -4) and (3, 8):

m = (8 - (-4)) / (3 - (-1)) = 12 / 4 = 3.

With the slope known, we can now use one of the points to find the y-intercept (c). Let's use the point (-1, -4):

y = mx + c becomes -4 = 3*(-1) + c, so c = -4 + 3 = -1.

Therefore, the equation of the line is y = 3x - 1.

Answer 2

i)(2,4)

ii)y=3x+c

Step-by-step explanation:

I. minus them from each other

ii. draw out the graph to find the gradient, which is rise over run, this is your m and c can be any number since it is a never ending straight line.