Final answer:
To graph points (1, 4) and (-2, 6) and the line that passes through them, each point is plotted on a graph, and a line is drawn connecting them to show the linear relationship between x and y. The slope and y-intercept of the line can be calculated to determine the equation representing this relationship.
Step-by-step explanation:
To graph points that represent the dependence of y on x, you start by plotting each individual point on a Cartesian coordinate system. The question asks to graph the points (1, 4) and (-2, 6). First, place a dot where x is 1 and y is 4, and then another where x is -2 and y is 6. After plotting these points, draw a straight line through them which represents the linear relationship between x and y values.
To determine the equation of this line, you can use the formula for slope (m), where m = (y2 - y1) / (x2 - x1). Apply the formula to the given points to find the slope. Once the slope is known, use either point to solve for the y-intercept (b) in the equation y = mx + b. With m and b known, you can write the full equation for the line and use it to predict other points along the line if needed. The drawing of the line and the calculation of its equation demonstrate how the value of y depends on x.