Final answer:
a) The equation of the line with slope m = 3/4 passing through the point (-1,-3) is y = 3/4x - 9/4.
b) To find the x-intercept of the line with equation y = 3/4x - 3, set y to zero and solve for x. The x-intercept is at (4,0).
Step-by-step explanation:
a) To determine the equation of a line given its slope m = 3/4 and passing through the point (-1,-3), we use the point-slope form of a linear equation, y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point.
Substituting (-1,-3) and m = 3/4 into the equation, we get y - (-3) = 3/4(x - (-1)), which simplifies to y + 3 = 3/4(x + 1). Further manipulation yields the final equation y = 3/4x - 9/4.
b) To find the x-intercept of the line with equation y = 3/4x - 3, we set y to zero since the x-intercept occurs when y = 0. Substituting y = 0 into the equation gives us 0 = 3/4x - 3. Solving for x by isolating x yields x = 4. Therefore, the x-intercept of the line is at the point (4,0). This means that the line crosses the x-axis at x = 4 when y is zero, signifying the x-intercept.