determine the equation of each line:
a) slope 3.4 passing through point (-2, -4)
b) slope -5 and y-intercept -0.7
a. m = 3.4, P(-2,-4).
Y = mx + b.
3.4*(-2) + b = -4
-6.8 + b = -4
b = 2.8 = y-int.
Eq: Y = 3.4x + 2.8.
b. m = -5, y-int = -0.7.
Y = mx + b.
Eq: Y = -5x - 0.7.
To determine the equation of a line, you can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Given the information given in the question:
a) To find the equation of a line with a given slope (m) passing through a specific point (x1, y1), follow these steps:
1. Substitute the given slope (m) into the slope-intercept form equation: y = mx + b.
2. Substitute the coordinates of the given point (-2, -4) into the equation: -4 = 3.4(-2) + b.
3. Solve for the y-intercept (b):
-4 = -6.8 + b
-4 + 6.8 = b
2.8 = b
4. Substitute the slope (m = 3.4) and the y-intercept (b = 2.8) back into the equation: y = 3.4x + 2.8.
Therefore, the equation of the line is y = 3.4x + 2.8.
b) To find the equation of a line with a specified slope (m) and y-intercept (b), follow these steps:
1. Substitute the given slope (-5) and y-intercept (-0.7) into the slope-intercept form equation: y = mx + b.
2. Substitute the values into the equation: y = -5x - 0.7.
Therefore, the equation of the line is y = -5x - 0.7.