Question

question
what is an equation of the line that passes through the points (-4, -3) and (8, 6)?

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1=-4\), \(y_1 = - 3\), \(x_2 = 8\), \(y_2=6\).
So, \(m=\frac{6-(-3)}{8 - (-4)}=\frac{6 + 3}{8 + 4}=\frac{9}{12}=\frac{3}{4}\).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Let's use the point \((-4,-3)\) and \(m = \frac{3}{4}\).
Substitute into the formula: \(y-(-3)=\frac{3}{4}(x - (-4))\)
Simplify: \(y + 3=\frac{3}{4}(x + 4)\)
Expand the right - hand side: \(y+3=\frac{3}{4}x+3\)
Subtract 3 from both sides: \(y=\frac{3}{4}x\)
We can also write it in standard form. Multiply both sides by 4: \(4y = 3x\), or \(3x-4y = 0\). But the slope - intercept form \(y=\frac{3}{4}x\) is also correct. If we use the other point \((8,6)\) to verify:
Substitute \(x = 8\) into \(y=\frac{3}{4}x\), we get \(y=\frac{3}{4}\times8 = 6\), which matches the point \((8,6)\). And when \(x=-4\), \(y=\frac{3}{4}\times(-4)=-3\), which matches the point \((-4,-3)\).

Answer:

The equation of the line is \(y=\frac{3}{4}x\) (or \(3x - 4y=0\))