Identify the slope of a line that passes through point (4, 1) and has a \( y \) intercept of 4

To find the slope of a line, we can use the slope-intercept form of the equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Given that the y-intercept \( b \) is 4, we have: \[ y = mx + 4 \] To find the slope (\( m \)), we can plug in the coordinates of the point (4, 1): \[ 1 = m(4) + 4 \] Now, solving for \( m \): \[ 1 - 4 = 4m \] \[ -3 = 4m \] \[ m = -\frac{3}{4} \] So the slope of the line is -\( \frac{3}{4} \). Here’s a fun fact: the concept of slope isn't just limited to lines on a graph; you can visualize it as how steep a hill is! A slope of -\( \frac{3}{4} \) means for every 4 units you move to the right, you would go down 3 units—think of a sliding slide that’s just a bit steep! Also, if you picture a coordinate grid, the slope can tell you which way your line is tilting. Positive slopes rise from left to right, while negative slopes (like ours!) fall as you move along. You can easily find slopes of other lines by comparing their points too. It’s like a secret code of angles!