Write an equation of the line satisfying the given conditions in standard form. How do you do this?
contains (-4, 0.3) and (3, -3.4)
Find the gradient and then substitue the gradient with 1 set of coordinates in the equation of a straight line.
To write the equation of a line, we typically use the point-slope form or the slope-intercept form. In this case, we can use the point-slope form which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line. We have two points: (-4, 0.3) and (3, -3.4).
Step 1: Determine the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we have:
m = (-3.4 - 0.3) / (3 - (-4))
m = (-3.7) / (7)
m = -3.7/7
So, the slope (m) is -3.7/7.
Step 2: Choose one of the points, say (-4, 0.3), and substitute the values of x1, y1, and m into the point-slope form.
Using the point-slope form with (-4, 0.3), we have:
y - 0.3 = (-3.7/7)(x - (-4))
y - 0.3 = (-3.7/7)(x + 4)
Step 3: Simplify the equation and convert it to the standard form (ax + by = c).
Multiply both sides of the equation by 7 (to eliminate the fraction):
7(y - 0.3) = (-3.7)(x + 4)
7y - 2.1 = -3.7x - 14.8
Rearranging the equation in standard form:
3.7x + 7y = -12.7
Therefore, the equation of the line satisfying the given conditions in standard form is 3.7x + 7y = -12.7.