Please help me to solve this problem. Thank you in advance for helping to solve this problem. Have a great day. Here is the question? Find an equation of the line that passes through the two given points. Write the equation in slope-intercept form, if possible.
Passes through (-3,0) and (3,1)
slope = (1-0)/(3-(-3)) = 1/6
so y = (1/6)x + b
plug in (-3,0)
0 = (1/6)(-3) + b
b = 1/2
y = (1/6)x + 1/2
To find the equation of a line passing through two given points in the slope-intercept form (y = mx + b), we need to determine the slope of the line (m) and the y-intercept (b).
Step 1: Determine the slope (m)
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given the two points (-3,0) and (3,1), we can substitute the values into the formula:
m = (1 - 0) / (3 - (-3))
m = 1 / 6
Therefore, the slope (m) of the line is 1/6.
Step 2: Determine the y-intercept (b)
To find the y-intercept (b), we can use the slope-intercept form and substitute the coordinates of one of the points into the equation. Let's use the point (-3, 0):
y = mx + b
0 = (1/6)(-3) + b
0 = -1/2 + b
To isolate b, we can add 1/2 to both sides:
b = 1/2
Therefore, the y-intercept (b) of the line is 1/2.
Step 3: Write the equation of the line
Now that we have the slope (m) and the y-intercept (b), we can write the equation in slope-intercept form:
y = mx + b
y = (1/6)x + 1/2
Therefore, the equation of the line passing through the points (-3,0) and (3,1) in slope-intercept form is y = (1/6)x + 1/2.
I hope this explanation helps you understand how to solve this problem! If you have any further questions, feel free to ask.